87 lines
1.9 KiB
Markdown
87 lines
1.9 KiB
Markdown
---
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id: 5a23c84252665b21eecc7edf
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title: Least common multiple
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challengeType: 5
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forumTopicId: 302301
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---
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# --description--
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The least common multiple of 12 and 18 is 36, because 12 is a factor (12 × 3 = 36), and 18 is a factor (18 × 2 = 36), and there is no positive integer less than 36 that has both factors. As a special case, if either *m* or *n* is zero, then the least common multiple is zero. One way to calculate the least common multiple is to iterate all the multiples of *m*, until you find one that is also a multiple of *n*. If you already have *gcd* for [greatest common divisor](<https://rosettacode.org/wiki/greatest common divisor>), then this formula calculates *lcm*. ( \\operatorname{lcm}(m, n) = \\frac{|m \\times n|}{\\operatorname{gcd}(m, n)} )
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# --instructions--
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Compute the least common multiple of an array of integers. Given *m* and *n*, the least common multiple is the smallest positive integer that has both *m* and *n* as factors.
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# --hints--
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`LCM` should be a function.
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```js
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assert(typeof LCM == 'function');
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```
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`LCM([2, 4, 8])` should return a number.
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```js
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assert(typeof LCM([2, 4, 8]) == 'number');
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```
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`LCM([2, 4, 8])` should return `8`.
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```js
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assert.equal(LCM([2, 4, 8]), 8);
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```
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`LCM([4, 8, 12])` should return `24`.
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```js
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assert.equal(LCM([4, 8, 12]), 24);
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```
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`LCM([3, 4, 5, 12, 40])` should return `120`.
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```js
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assert.equal(LCM([3, 4, 5, 12, 40]), 120);
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```
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`LCM([11, 33, 90])` should return `990`.
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```js
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assert.equal(LCM([11, 33, 90]), 990);
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```
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`LCM([-50, 25, -45, -18, 90, 447])` should return `67050`.
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```js
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assert.equal(LCM([-50, 25, -45, -18, 90, 447]), 67050);
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```
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# --seed--
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## --seed-contents--
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```js
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function LCM(A) {
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}
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```
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# --solutions--
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```js
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function LCM(A) {
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var n = A.length,
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a = Math.abs(A[0]);
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for (var i = 1; i < n; i++) {
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var b = Math.abs(A[i]),
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c = a;
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while (a && b) {
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a > b ? (a %= b) : (b %= a);
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}
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a = Math.abs(c * A[i]) / (a + b);
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}
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return a;
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}
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```
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